Bending, entropy and proper affine actions of surface groups

Martin Bridgeman; Richard Canary; Andres Sambarino

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arXiv · 2602.20146

Bending, entropy and proper affine actions of surface groups

Martin Bridgeman·Richard Canary·Andres Sambarino

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Abstract

We show that for any closed surface $S$ there is an explict neighborhood $V$ of the fuchsian locus in quasifuchsian space $\mathsf{QF}(S)$ such that for every representation $\rho\in V$ which is not fuchsian, there is a proper affine action on $\mathfrak{sl}(2,\mathbb{C})$ with linear part $\mathsf{Ad}(\rho)$. We further show that there is a larger neighborhood $U$ of the Fuchsian locus so that every critical point of the entropy function in $U$ lies on the Fuchsian locus.

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BibTeX RIS

Martin Bridgeman, Richard Canary, Andres Sambarino. 2026-02-23. Bending, entropy and proper affine actions of surface groups. https://arxiv.org/abs/2602.20146

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